As presented at the University of Milan on 2022-02-21HEADv1.0master

7 files changed, 140 insertions, 0 deletions

diff --git a/figs/energy_relative_error.fig/2020-10-15+energy.dat b/figs/energy_relative_error.fig/2020-10-15+energy.dat
new file mode 100644
index 0000000..8a6566c
--- /dev/null
+++ b/figs/energy_relative_error.fig/2020-10-15+energy.dat
@@ -0,0 +1,13 @@
+1e-6       7.90e-6     7.91e-6
+1e-4      8.344e-4    8.345e-4   0.017      0.018    8.355e-4      8.356e-4        0.015             0.016
+1e-3     9.1338e-3   9.1339e-3   0.048      0.049    9.142e-3      9.143e-3        0.045             0.046
+5e-3     5.0613e-2   5.0614e-2   0.080      0.081   5.0648e-2     5.0649e-2        0.070             0.071
+1e-2    1.06107e-1  1.06108e-1   0.087      0.088   1.0627e-1     1.0628e-1        0.073             0.074
+1.5e-2   1.6337e-1   1.6338e-1   0.090      0.091   1.6342e-1     1.6343e-1        0.088             0.089
+2e-2     2.2162e-1   2.2163e-1   0.093      0.094   2.2169e-1     2.2170e-1        0.090             0.091
+5e-2     5.8044e-1   5.8045e-1   0.091      0.092   5.8046e-1     5.8047e-1        0.091             0.092
+1e-1     1.1918e+0   1.1919e+0   0.088      0.089   1.1919e+0     1.1920e+0        0.085             0.086
+1e-0     1.2430e+1   1.2431e+1   0.058      0.059    1.245e+1      1.246e+1         0.05              0.06
+1e+1     1.2544e+2   1.2545e+2   0.031      0.032
+5e+1     6.2803e+2   6.2804e+2    0.02       0.03
+
diff --git a/figs/energy_relative_error.fig/Makefile b/figs/energy_relative_error.fig/Makefile
new file mode 100644
index 0000000..93e03f5
--- /dev/null
+++ b/figs/energy_relative_error.fig/Makefile
@@ -0,0 +1,51 @@
+PROJECTNAME=cmp_energy1
+
+SIMPLEQ=~/Work/Research/2018+bose_gas/cmp/simpleq
+
+DATS= simpleq1.dat mueq1.dat bigeq1.dat
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
+
+all: $(PDFS)
+
+$(PDFS): $(DATS)
+	gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
+	pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
+
+bigeq1.dat:
+	for rho in 1e-6 1e-4 1e-3 5e-3 1e-2 1.5e-2 2e-2 5e-2 1e-1 1.0 1e1 5e1; do \
+	  echo -n $$rho "  " >> $@-tmp ;\
+	  julia $(SIMPLEQ)/main.jl -p "N=12;P=8;J=10;maxiter=100;v_a=1;rho=$$rho;minlrho=-6;nlrho=50;eq=bigeq" -M medeq energy >> $@-tmp ;\
+	done
+	paste $@-tmp 2020-10-15+energy.dat > $@
+	rm $@-tmp
+simpleq1.dat:
+	for lrho in -6 -4 -3 -2.3010299956639813 -2 -1.8239087409443189 -1.6989700043360187 -1.3010299956639813 -1 0 1 1.6989700043360187; do\
+	  julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=1;minlrho=$$lrho;nlrho=1" -M simpleq energy_rho >> $@-tmp ;\
+	done
+	paste $@-tmp 2020-10-15+energy.dat > $@
+	rm $@-tmp
+mueq1.dat:
+	for lrho in -6 -4 -3 -2.3010299956639813 -2 -1.8239087409443189 -1.6989700043360187 -1.3010299956639813 -1 0 1 1.6989700043360187; do\
+	  julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=1;minlrho=$$lrho;nlrho=1" -M mueq energy_rho >> $@-tmp ;\
+	done
+	paste $@-tmp 2020-10-15+energy.dat > $@
+	rm $@-tmp
+
+
+install: $(PDFS)
+	cp $^ $(INSTALLDIR)/
+
+clean-aux:
+	rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
+	rm -f $(addsuffix .aux, $(PROJECTNAME))
+	rm -f $(addsuffix .log, $(PROJECTNAME))
+
+clean-dat:
+	rm -f $(DATS)
+	rm -f Abar.dat
+
+clean-tex:
+	rm -f $(PDFS)
+
+clean: clean-aux clean-tex
diff --git a/figs/energy_relative_error.fig/bigeq1.dat b/figs/energy_relative_error.fig/bigeq1.dat
new file mode 100644
index 0000000..ccab7cc
--- /dev/null
+++ b/figs/energy_relative_error.fig/bigeq1.dat
@@ -0,0 +1,13 @@
+1e-6    7.933345669932108e-06  1.702110068633820e-12	1e-6       7.90e-6     7.91e-6
+1e-4    8.349333596092273e-04  1.112527655484278e-13	1e-4      8.344e-4    8.345e-4   0.017      0.018    8.355e-4      8.356e-4        0.015             0.016
+1e-3    9.146316224214820e-03  2.077370190827862e-12	1e-3     9.1338e-3   9.1339e-3   0.048      0.049    9.142e-3      9.143e-3        0.045             0.046
+5e-3    5.063551121414726e-02  8.398015568932763e-12	5e-3     5.0613e-2   5.0614e-2   0.080      0.081   5.0648e-2     5.0649e-2        0.070             0.071
+1e-2    1.061166635113156e-01  5.017547334745932e-15	1e-2    1.06107e-1  1.06108e-1   0.087      0.088   1.0627e-1     1.0628e-1        0.073             0.074
+1.5e-2    1.633545333357252e-01  2.212732350724188e-15	1.5e-2   1.6337e-1   1.6338e-1   0.090      0.091   1.6342e-1     1.6343e-1        0.088             0.089
+2e-2    2.216006926766234e-01  4.554921896809050e-15	2e-2     2.2162e-1   2.2163e-1   0.093      0.094   2.2169e-1     2.2170e-1        0.090             0.091
+5e-2    5.805467427278628e-01  3.333614946727334e-15	5e-2     5.8044e-1   5.8045e-1   0.091      0.092   5.8046e-1     5.8047e-1        0.091             0.092
+1e-1    1.191928562890024e+00  2.450444415773880e-15	1e-1     1.1918e+0   1.1919e+0   0.088      0.089   1.1919e+0     1.1920e+0        0.085             0.086
+1.0    1.243051761633436e+01  3.791416729017179e-12	1e-0     1.2430e+1   1.2431e+1   0.058      0.059    1.245e+1      1.246e+1         0.05              0.06
+1e1    1.254476421597336e+02  2.677873467933947e-13	1e+1     1.2544e+2   1.2545e+2   0.031      0.032
+5e1 nan nan	5e+1     6.2803e+2   6.2804e+2    0.02       0.03
+	
diff --git a/figs/energy_relative_error.fig/cmp_energy1.gnuplot b/figs/energy_relative_error.fig/cmp_energy1.gnuplot
new file mode 100644
index 0000000..c2b1afd
--- /dev/null
+++ b/figs/energy_relative_error.fig/cmp_energy1.gnuplot
@@ -0,0 +1,37 @@
+set title "$v(\\mathbf x)=e^{-|\\mathbf x|}$"
+set ylabel "energy relative error" offset +3
+set xlabel "$\\rho$"
+
+set xtics 1e-6, 100, 100
+set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
+unset mxtics
+set xrange [1e-6:1e2]
+
+set ytics 1e-5, 10, 1e-1
+set ytics add ("$10^{-5}$" 1e-5, "$10^{-4}$" 1e-4, "$10^{-3}$" 1e-3, "$10^{-2}$" 1e-2, "$10^{-1}$" 1e-1)
+set yrange [1e-5:1e-1]
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+unset key
+
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 2
+set style line 2 linetype rgbcolor "#DC143C" linewidth 2
+set style line 3 linetype rgbcolor "#32CD32" linewidth 2
+set style line 4 linetype rgbcolor "#4B0082" linewidth 2
+set style line 5 linetype rgbcolor "#DAA520" linewidth 2
+
+set pointsize 1
+
+max(x,y)=(x>y ? x : y)
+
+set logscale xy
+
+plot \
+ "simpleq1.dat" using 1:($3<1e-5 ? max(abs($2-$5)/$5,abs($2-$6)/$6) : 1/0) every ::1 with lp ls 1 ,\
+ "bigeq1.dat" using 1:($3<1e-5 ? max(abs($2-$5)/$5,abs($2-$6)/$6) : 1/0) every ::1 with lp ls 4 ,\
+ "2020-10-15+energy.dat" using 1:(max(max(abs($6-$2)/$2,abs($6-$3)/$3),max(abs($7-$2)/$2,abs($7-$3)/$3))) every ::1 with lp ls 2
+
diff --git a/figs/energy_relative_error.fig/cmp_energy1.pdf b/figs/energy_relative_error.fig/cmp_energy1.pdf
new file mode 100644
index 0000000..601b146
--- /dev/null
+++ b/figs/energy_relative_error.fig/cmp_energy1.pdf
diff --git a/figs/energy_relative_error.fig/mueq1.dat b/figs/energy_relative_error.fig/mueq1.dat
new file mode 100644
index 0000000..6680ed3
--- /dev/null
+++ b/figs/energy_relative_error.fig/mueq1.dat
@@ -0,0 +1,13 @@
+ 1.000000000000000e-06  7.934286257047026e-06  3.235575358862730e-14	1e-6       7.90e-6     7.91e-6
+ 1.000000000000000e-04  8.377752370367244e-04  3.201262322514326e-14	1e-4      8.344e-4    8.345e-4   0.017      0.018    8.355e-4      8.356e-4        0.015             0.016
+ 1.000000000000000e-03  9.227516472314044e-03  5.926882960328585e-12	1e-3     9.1338e-3   9.1339e-3   0.048      0.049    9.142e-3      9.143e-3        0.045             0.046
+ 4.999999999999999e-03  5.110614907540598e-02  1.069784208067329e-14	5e-3     5.0613e-2   5.0614e-2   0.080      0.081   5.0648e-2     5.0649e-2        0.070             0.071
+ 1.000000000000000e-02  1.069255387977072e-01  1.572627931557844e-14	1e-2    1.06107e-1  1.06108e-1   0.087      0.088   1.0627e-1     1.0628e-1        0.073             0.074
+ 1.500000000000000e-02  1.643925118385577e-01  2.494863657028789e-14	1.5e-2   1.6337e-1   1.6338e-1   0.090      0.091   1.6342e-1     1.6343e-1        0.088             0.089
+ 2.000000000000000e-02  2.228019992986293e-01  1.448625206361080e-14	2e-2     2.2162e-1   2.2163e-1   0.093      0.094   2.2169e-1     2.2170e-1        0.090             0.091
+ 5.000000000000000e-02  5.821600306289594e-01  2.429130993459621e-14	5e-2     5.8044e-1   5.8045e-1   0.091      0.092   5.8046e-1     5.8047e-1        0.091             0.092
+ 1.000000000000000e-01  1.193625606724180e+00  9.289627651289616e-14	1e-1     1.1918e+0   1.1919e+0   0.088      0.089   1.1919e+0     1.1920e+0        0.085             0.086
+ 1.000000000000000e+00  1.243092200540192e+01  3.956891809887943e-12	1e-0     1.2430e+1   1.2431e+1   0.058      0.059    1.245e+1      1.246e+1         0.05              0.06
+ 1.000000000000000e+01  1.254464788052155e+02  1.136222076562384e-14	1e+1     1.2544e+2   1.2545e+2   0.031      0.032
+ 4.999999999999999e+01  6.280479158155819e+02  4.085062088184932e-15	5e+1     6.2803e+2   6.2804e+2    0.02       0.03
+	
diff --git a/figs/energy_relative_error.fig/simpleq1.dat b/figs/energy_relative_error.fig/simpleq1.dat
new file mode 100644
index 0000000..0a9946c
--- /dev/null
+++ b/figs/energy_relative_error.fig/simpleq1.dat
@@ -0,0 +1,13 @@
+ 1.000000000000000e-06  7.934458317554763e-06  1.386474846476237e-14	1e-6       7.90e-6     7.91e-6
+ 1.000000000000000e-04  8.392960650211980e-04  4.992772141681879e-14	1e-4      8.344e-4    8.345e-4   0.017      0.018    8.355e-4      8.356e-4        0.015             0.016
+ 1.000000000000000e-03  9.335885024335848e-03  9.476600935679491e-12	1e-3     9.1338e-3   9.1339e-3   0.048      0.049    9.142e-3      9.143e-3        0.045             0.046
+ 4.999999999999999e-03  5.253256909806337e-02  2.904203225041083e-14	5e-3     5.0613e-2   5.0614e-2   0.080      0.081   5.0648e-2     5.0649e-2        0.070             0.071
+ 1.000000000000000e-02  1.105504827786785e-01  3.695967730970493e-14	1e-2    1.06107e-1  1.06108e-1   0.087      0.088   1.0627e-1     1.0628e-1        0.073             0.074
+ 1.500000000000000e-02  1.702888708763101e-01  2.044316796426063e-14	1.5e-2   1.6337e-1   1.6338e-1   0.090      0.091   1.6342e-1     1.6343e-1        0.088             0.089
+ 2.000000000000000e-02  2.309054339970606e-01  1.984104771646051e-14	2e-2     2.2162e-1   2.2163e-1   0.093      0.094   2.2169e-1     2.2170e-1        0.090             0.091
+ 5.000000000000000e-02  6.014214358150070e-01  1.045253287889987e-14	5e-2     5.8044e-1   5.8045e-1   0.091      0.092   5.8046e-1     5.8047e-1        0.091             0.092
+ 1.000000000000000e-01  1.226000446492040e+00  3.630493925691041e-15	1e-1     1.1918e+0   1.1919e+0   0.088      0.089   1.1919e+0     1.1920e+0        0.085             0.086
+ 1.000000000000000e+00  1.253044200066420e+01  1.230015282154983e-13	1e-0     1.2430e+1   1.2431e+1   0.058      0.059    1.245e+1      1.246e+1         0.05              0.06
+ 1.000000000000000e+01  1.256270224354739e+02  6.086298884133178e-15	1e+1     1.2544e+2   1.2545e+2   0.031      0.032
+ 4.999999999999999e+01  6.282817756461592e+02  1.506690451671515e-15	5e+1     6.2803e+2   6.2804e+2    0.02       0.03
+